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Master the Art of Simplifying Radicals: Step-by-Step Guide

PC20.1

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

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Solving absolute value equations

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

PC20.10

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

Sigma notation

PC20.11

Graphing reciprocals of linear functions

Graphs of rational functions

Graphing reciprocals of quadratic functions

PC20.2

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Multiplying radicals

Rationalize the denominator

PC20.3

Solving rational equations

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Applications of rational equations

PC20.4

Unit circle

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

PC20.5

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

PC20.6

Factoring difference of cubes

Factoring sum of cubes

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

PC20.7

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Completing the Square

PC20.8

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

PC20.9

Solving quadratic inequalities

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Pre-Calculus 20

Number Sense

math

Intro

Ex. 1:

Ex. 2:

Simplifying the fifth root of 1/32 using prime factorization

Evaluating the fourth root of 10,000 by prime factoring

Evaluating the 7th root of 4365 using two calculator methods

Evaluating a negative fifth root using a calculator

Simplifying radicals using prime factorization

To simplify <a href='[[glossary.html|{"keyword":"Radical"}]]'>radicals</a>, we will need to find the prime factorization of the number inside the radical sign first. Then, move each group of prime factors outside the radical according to the index. The last step is to simplify the expression by multiplying the numbers both inside and outside the radical sign.